Ecological Engineering 82 (2015) 222–230
Contents lists available at ScienceDirect
Ecological Engineering
journal homepage: www.elsevier.com/locate/ecoleng
Method for synchronisation of soil and root behaviour for assessment
of stability of vegetated slopes
Guillermo Tardío a, * , Slobodan B. Mickovski 1,b
a
b
Technical University of Madrid, Avenida Niceto Alcalá Zamora, 6, 4D, 28905 Getafe (Madrid), Spain
School of Engineering and Built Environment, Glasgow Caledonian University, 70 Cowcaddens Rd., G4 0BA Glasgow, Scotland, UK
A R T I C L E I N F O
A B S T R A C T
Article history:
Received 26 January 2015
Received in revised form 2 April 2015
Accepted 28 April 2015
Available online xxx
A new methodology to incorporate the mechanical root anchorage effects in both short- and long-term
slope stability analysis is proposed based on observed and assumed behaviour of rooted soil during shear
failure.
The main focus of the present work is the stress–strain range comparison for both soil and roots and
development of a stability model that would incorporate relevant root and soil characteristics based on
the fact that available soil–root composite shear resistance depends on the magnitude of the shear strain.
This new approach, combining stress–strain analysis, continuum mechanics, and limit equilibrium
stability assessment, allows for a more realistic simulation of the rooted soil composite whereby the
stabilising effect of the rooted soil is incorporated in the slope stability calculations by means of the
synchronisation of root and soil mechanical behaviour during failure.
The stability of vegetated terraces in a study area in Spain is used as a case study to demonstrate the
proposed methodology and to compare the results with the traditional use of the perpendicular root
reinforcement model. The results of the study show that as the shear displacement (strain) increases, the
stress is transferred from the soil that provides most of the resistance at low strains onto the roots that
provide the most of the resistance to shear at high strains. Including this behaviour in the overall
resistance to failure of the root–soil continuum resulted in a more conservative and realistic assessment
of the stability of a vegetated slope immediately after a precipitation event when a progressive failure is
most likely to be triggered.
ã 2015 Elsevier B.V. All rights reserved.
Keywords:
Soil reinforcement
Rooted soil
Strain compatibility
Finite element method
Slope stability
Vegetated slope
Eco-technology
1. Introduction
The development and use of plant root reinforcement models to
assess the effects of vegetation in slope stability analysis has
become a prominent research area all over the world in the last 10
years with research developments in root anchorage models
(Pollen and Simon, 2005; Norris et al., 2008; Stokes et al., 2009;
Preti and Giadrossich, 2009; Schwarz et al., 2010; Fan, 2012;
Bourrier et al., 2013) and their application in practical stability
problems such as shallow landslides or soil erosion (Coppin and
Richards, 2007; Danjon et al., 2007; Schwarz et al., 2010; Comino
and Druetta, 2009; Mickovski and van Beek, 2009; Thomas and
Pollen-Bankhead, 2010).
* Corresponding author. Tel.: +34 91 172 83 60.
E-mail addresses: [email protected] (G. Tardío),
[email protected] (S.B. Mickovski).
1
Tel.: +44 141 2731105.
http://dx.doi.org/10.1016/j.ecoleng.2015.04.101
0925-8574/ ã 2015 Elsevier B.V. All rights reserved.
From a mechanical point, rooted soil behaviour can be
simulated by using different root reinforcement models. Some
of them are based on traditional limit equilibrium (LE) approaches
(e.g. Greenwood, 2006), other are based on more advanced
numerical analysis (e.g. Dupuy et al., 2007; Bourrier et al., 2013).
The most common mechanical root reinforcement models are the
perpendicular and inclined root reinforcement model (Wu et al.,
1979; Gray and Leiser, 1982), the fibre bundle model (Pollen and
Simon, 2005; Schwarz et al., 2010), the energy approach model
(Ekanayake et al., 1997) and a number of LE, finite element (FE), and
finite difference (FD) numerical methods integrating the above
models (Gray and Sotir, 1996; Chok et al., 2004; Fourcaud et al.,
2007; Briggs, 2010; Mickovski et al., 2011; Bourrier et al., 2013).
All of the above approaches consider a composite material
comprising soil matrix and roots and, therefore, must include two
different mechanical behaviours in the analysis. Although attempts
have been made in the past to account for this (Dupuy et al., 2007;
Lin et al., 2010; Bourrier et al., 2013), the modelled root system and
soil properties were either assumed or simplified to suit the
particular model which made it difficult for practical application.
G. Tardío, S.B. Mickovski / Ecological Engineering 82 (2015) 222–230
The existing strain based rooting models (e.g. fibre bundle model,
root bundle model) have simulated the failure mechanisms of a
group of roots without accounting for varying strength of the
materials at different strains which are important in both the
rooted soil simulation and the stability analyses at a slope scale. To
exceed these limitations, there is a need for a methodology that
would combine the simplicity of the LE approach while
incorporating continuum mechanics concepts and strain compatibility within the realistically modelled soil–root composite in
order to provide the basis for wider, practical application.
Similar to the geosynthetic reinforcements used in geoenvironmental engineering, plant roots enhance the soil strength
by transferring shear stresses from the soil onto the roots that, due
to different elastic properties, are better suited to resist it
(Mickovski et al., 2009). It is conceivable that, as with other
reinforcement elements, in the case of rooted soil the strain level
corresponding to the root peak strength is higher than the one for
soil peak strength due to differences in elastic properties of the
roots and the soil. Although this premise has been investigated in
the past for other composite materials (Jewell and Milligan, 1989;
Prisco and Nova, 1993; Morel and Gourc, 1997; Zornberg, 2002;
Hatami and Bathurst, 2006; Michalowski, 2008; Jonathan et al.,
2013), it has never been explored in the context of sustainable use
of vegetation for soil reinforcement.
Based on this concept, in this paper we propose a methodology
that takes advantage of both the design for stability and the strain
compatibility methodologies incorporating roots as reinforcing
elements. We illustrate our approach through application in a case
study of terraced slopes in Spain exhibiting instability and compare
the results of this analysis with the results from other existing
models.
The aim of this paper is to propose a practical framework for
realistically accounting for the mechanical effect of roots on soil
reinforcement in the design for slope stability. The objectives are to
explore the behaviour of the soil–root continuum at failure
comparing it to the behaviour of a reinforced soil, and apply it into
the existing rooting models as an input into a LE slope stability
analysis. Linking the soil and roots strain in an iso-strain state
(equality of strain of both soil and roots) of the root–soil continuum
and demonstrating its application in a representative case study
not only provides a more realistic representation of the root–soil
interaction in terms of stress transfer processes and soil
reinforcement, but also provides a mode of application of relatively
easily measured and analysed parameters into stability assessment
of vegetated slopes which, in turn, could increase the confidence of
practitioners about the use of eco-technological solutions.
223
continuum (roots and soil) that have differing elastic properties
have to be made compatible before including them in Eq. (1).
In the case of Mohr–Coulomb failure criterion (Smith and
Smith, 1998), the soil shear strength t [kN/m2] is expressed in
terms of its cohesion c [kN/m2] and its internal friction angle ’ [ ]
for different normal stress s [kN/m2].
t ¼ c þ s tgðfÞ
(2)
The values of both cohesion and internal friction angle shown in
Eq. (2) can be either peak or residual depending on the level of
strain (Fig. 1), but in the case of reinforced soils, the strain level at
which extensible reinforcements may develop their peak values
will usually be higher than the strain when the soil develops its
peak value (Leshchinsky, 2002; Schwarz et al., 2010). This is
particularly true for small diameter roots which can be considered
as flexible reinforcements (Wu et al., 1979; Mickovski et al., 2007),
and which provide ductility for the root–soil continuum, reaching
the peak strength at high strains (e.g. Mickovski et al., 2007;
Mickovski and van Beek, 2009). This suggests that at high strain
(displacement) level the soil may be developing its residual
strength value while, at the same time, the roots (reinforcements)
are developing their peak strength—a concept which has to be
taken into account in the analysis of slope stability and factor of
safety calculation for vegetated soil.
The reinforcement effect due to the plant roots (excluding the
major structural roots) can be expressed in terms of an “added
cohesion” DS which is added on to the strength of the non-rooted
soil (Eq. (2)) and can be calculated, for example, for a known root
tensile strength tR [KN/m2] and root area ratio (RAR; the ratio of
area of roots crossing the shear plane and shear plane area;
Waldron (1977) and Wu et al. (1979); Eq. (3)) as:
DS ¼ 1:2tR
(3)
To make the soil and root mechanical behaviour compatible, the
displacement at which the soil reaches its peak strength can be
linked to the corresponding root elongation (Shewbridge and Sitar,
1985; Abe and Ziemer, 1991) as:
e ¼ ð1 þ B2 b2 e2bx Þ1=2 1
(4)
where e = root strain [mm/mm]; x = shear displacement [mm];
B = half of the shear displacement [mm]; b = coefficient depending
on root diameter D [mm] and RAR (Abe and Ziemer, 1991)
expressed as:
b ¼ 0:2262 0:0715RAR 0:0016D
(5)
2. Material and methods
2.1. Background
Safety Factor ðSFÞ ¼
Available Strength
Required strength
(1)
To realistically model the behaviour of a composite material such
as the soil permeated with roots, the different contributions to the
strength of the root–soil continuum by the elements of the
Peak strength
STRESS
In traditional slope safety factor (SF) calculation (Eq. (1); Zheng
et al., 2006) for a slope to be safe, the SF has to be greater than unity
(SF > 1), i.e. the available strength (e.g. by the root–soil continuum)
has to be greater than the required strength. At the same time, all
terms included in the numerator are assumed to have compatible
stress–strain behaviour (similar development of stresses in all
elements at any strain level), while the effects included in the
denominator do not depend on the strain level (Leshchinsky, 1997).
Residual strength
DISPLACEMENT
Fig. 1. Typical behaviour of soil under shear. The stress-displacement curve of a
non-reinforced soil shows that as the displacement increases, the soil stress
increases up to the soil peak shear strength value before decreasing and levelling off
to the residual soil shear strength value at very large displacements.
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G. Tardío, S.B. Mickovski / Ecological Engineering 82 (2015) 222–230
With known strain and elastic modulus of the roots, the tensile
strength can be calculated from Hookés law for known RAR at the
shear surface (Eq. (6)) which will ultimately help to calculate the
synchronised additional cohesion due to roots (Eq. (3)):
tR ¼ eERAR ¼ s RAR
(6)
where s is the mobilised root tensile strength corresponding to e.
2.2. Approach/methodology
In traditional reinforced soil engineering, long-term (peak)
strength design value for the reinforcement is chosen in such a way
that it will be mobilised at a strain value corresponding to the soil
peak strength (Berardi and Pinzani, 2008). The strength values of
the composite material elements are synchronized within the
limited strains (or displacements). This situation justifies the use of
soil strength peak values in safety factor calculations for newly
designed reinforced soil slopes.
In natural vegetated slope cases, strains are not limited and
failures occur gradually over a large range of strains in the longterm. Therefore, it is recommended to use soil residual strength
values in slope stability analysis (Jewell, 1990) while ensuring that
the long term design strength of the reinforcement (root strength)
is to be achieved at a strain level corresponding to the residual soil
strength. This is a necessary step for achieving strain compatibility
in slope stability formulae and a requirement of the methodology
proposed in the following sections. With this approach, a situation
with the entire shear surface working at soil peak strength
(traditional geotechnical engineering approach which is unrealistic due to lack of compatibility between mobilising and resisting
strength) will become a situation where a number of zones
progressively develop along the shear surface. In these zones, the
soil will resist failure with its residual strength due to large
displacements/strains. At the same time, the critical sliding surface
locally around the roots will be determined using soil peak
strength values due to the small displacements of the soil around
the roots that now provide the major resistance to the shear load/
stress.
2.3. Proposed methodology for stability assessment of a vegetated
slope
To capture the processes of initiation of a slope instability event,
development of a sliding surface and its progressive expansion
through to the failure of the root-slope continuum, first the stress
state local to the rooted soil should be analysed for a ‘local’ safety
factor (Krahn, 2004) in order to confirm the progressive failure in a
particular section of the rooted soil. The proposed methodology is
shown in Fig. 2 and described below.
STEP 1: establishing the stress distribution and values necessary for local safety factors calculation using finite element (FE)
stress analysis.
STEP 2: application of a LE method for global slope stability
assessment, using:
- The non-rooted soil peak shear strength value obtained from
laboratory or in situ shear tests;
Fig. 2. Flowchart of the proposed methodology. SFGLOBAL = global safety factor. SFLOCAL = local safety factor.
G. Tardío, S.B. Mickovski / Ecological Engineering 82 (2015) 222–230
225
Fig. 3. An example of finite element stability analysis using commercially available software (GEO-SLOPE/W International Ltd., 2014). Although the slope global safety factor
is 1.108, a local safety factor lower than one is shown to occur at the bottom of the shaded slice (SFL = 0.89) indicating that progressive failure phenomenon is likely to have
occurred. Local safety factors are checked throughout the critical sliding surface (step 3 of the proposed methodology).
- Root strength value corresponding to the strain level at which
the soil reaches its strength peak value (Eqs. (4), (6), and (3)), i.e.
linking soil displacement to root elongation (e.g. Abe and
Ziemer, 1991; Van Beek et al., 2005; Wu, 2006) to synchronise
soil and reinforcement stress–strain behaviour.
STEP 3: inspection along the critical slip surface derived from
the above analysis to identify any local safety factors indicating
failure (SFL < 1; Krahn, 2004) i.e. zones where a failure had
occurred locally. If none of the local SF is lower than one, the global
SF calculated in step 2 can be taken as definitive. If there are local
SFL < 1 along the critical slip surface, a progressive failure is likely
to have occurred at least in part of the slip surface and, as failure
progresses, the strength developed will be at or close to the soil
residual strength value (Fig. 3). The local safety factor can then be
re-calculated as:
SFi residual zone ¼
ROOT PEAK STRENGTH
ðSF DESTABILIZING Þ SOIL RESIDUAL STRENGTH
(7)
In this expression, it is assumed that the roots develop their
peak tensile strength value while the soil is mobilizing its residual
shear strength value due to large displacements/strains. Because
the soil residual strength has a constant value and it does not vary
with the strain level, Eq. (7) can be rearranged as:
SF DESTABILIZING ¼ Srequired
¼
ROOT PEAK STRENGTH
þ SOIL RESIDUAL STRENGTH
SF
(8)
The above shows that, at large displacements, the necessary
strength to achieve equilibrium is equal to the mobilized root
strength plus the residual strength of the soil (which operates fully
mobilized). The safety factor does not apply to the residual soil
strength because the soil strength is at its minimum (constant)
value after the phenomenon of progressive failure has occurred
and any extra stress would be transferred to the adjacent zones of
the shear surface.
The global safety factor (SFGLOBAL) for the slope in the zones
where SFL < 1 (i.e. the soil is resisting shear with its residual
strength value), and the SFL calculated using Eq. (7), can be
calculated as a weighted average using the slice lengths as the
weighting factor (Eq. (9)).
Fig. 4. An example of a failure surface divided into the residual zone (failure in soil occurred locally, soil resisting with residual shear strength) and the peak zone (no failure
occurred locally, soil resisting with peak shear strength) delineated using commercially available software (GEO-SLOPE/W International Ltd., 2014).
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G. Tardío, S.B. Mickovski / Ecological Engineering 82 (2015) 222–230
where li is the length of the ith slice.
The first term of the SFGLOBAL expression (Eq. (9)) is the sum of
local safety factors in the residual zone calculated according to
Eq. (7). The second term in the numerator refers to the peak zone of
the failure surface (Fig. 4). For cases where safety factor values are
very different (e.g. one of the safety factors is much higher than the
rest), a geometric mean would be suitable to use in order to avoid
bias in Eq. (9).
slopes with overall slope angles ranging between 45 and 70 . The
slope length was approximately 60 m, and long term monitoring
recorded potential instability connected to runoff and soil slippage
after intense rainfall events (Mickovski and van Beek, 2009). The
runoff from the slope contributed to the undermining of the slope
toe where the progressive failure initiated before migrating up the
slope and resulting in bulging mid-slope and soil mass depositing
at the toe (Fig. 5).
The slopes, comprising soil with Young’s modulus Es = 50 MPa
and Poisson’s ratio n = 0.33 measured in the laboratory, were
planted with rows of vetiver grass (Vetiveria zizanioides) in order to
mitigate the effects of slope instability. The spacing between the
rows of vetiver was approximately 0.3 m and their length between
3 m and 4 m. Root distribution with depth as well as root
morphological and physical properties (diameter and root tensile
strength) were recorded using block excavations and investigation
trenches. The vetiver roots had a root mean diameter of 0.75 mm,
permeated the soil vertically down to 0.3 m depth. The strength of
the rooted soil was measured using in situ direct shear tests
(Mickovski and van Beek, 2009) while the strength of the nonrooted soil was measured in the laboratory using standard shear
box apparatus (British Standards Institution (BSI), 1990). At the
shear surface developing during the shear tests, the RAR was
recorded as 0.04%. Roots were sampled from site and tested in
tension, yielding an average value of the root tensile strength of
tR = 4.91 MPa (Mickovski et al., 2005; Mickovski and van Beek,
2009) and an average Young’s modulus of elasticity of E = 1.0 GPa.
These parameters measured in situ or in the laboratory were
used as an input into a limit equilibrium analysis for slope stability
and the perpendicular root model (Wu et al., 1979) for root
reinforcement.
The software used to implement the proposed methodology
was SIGMA/W (step 1) and SLOPE/W (steps 2 and 3) (GEO-SLOPE/
W International Ltd., 2014). For comparability, the critical slip
surfaces obtained and reported in a previous analysis of the same
slope (Mickovski and van Beek, 2009) were analysed.
2.4. Case study (model validation)
3. RESULTS
We applied the proposed methodology to calculate the stability
of a series of terraced slopes exhibiting instability. The study site is
located near Almudaina, Spain (X = 729275 Y = 4293850 and
Z = 480 m on UTM 30 s) and comprises approximately 2.0 m high
3.1. Step 1
Fig. 5. Observed slope failure at the study site (Mickovski and van Beek, 2009).
Runoff over the slope contributed towards the loss of toe support, resulting in
bulging mid-slope and deposition of soil material at the toe of the slope.
SFGLOBAL ¼
ðSSFlocal li ÞRESIDUALZONE þ ðSSFlocal li ÞPEAKZONE þ
Sli
(9)
FE stress analysis using Sigma/W was carried out using the
elastic properties of the soil as shown in Fig. 6.
Fig. 6. Finite element stress analysis of the terraces using Sigma/W. Stresses are calculated in each node of the FE mesh based on soil elastic properties. Shaded areas show
vegetated terraces where roots contribute towards the strength with added cohesion.
G. Tardío, S.B. Mickovski / Ecological Engineering 82 (2015) 222–230
227
Table 1
Non-rooted soil peak properties used in determination of critical slip surface.
Short term analysis (undrained)
Long term analysis (drained)
Cohesion (kPa)
Angle of internal friction ( )
Cohesion (kPa)
Angle of internal friction ( )
Soil unit weight (kN/m3)
4.5
0
0
34.5
18
Table 2
Input parameters and synchronised added cohesion (cr) value corresponding to non-rooted soil peak shear displacement (x = 5 mm).
x (shear displacement) (mm)
B (mm)
b (mm1)
e (mm/mm)
E (GPa)
s (MPa)
RAR (%)
tR (kPa)
cr (kPa)
5.0
2.5
0.0222
9.8519 104
1.00
0.99
0.04
0.39
0.47
3.2. Step 2
Using Bishop’s LE method and stresses calculated in the
previous step, the critical slip surfaces for both long- and shortterm conditions of non-rooted soil (Table 1) were established,
yielding SF = 1.01 and SF < 1 for the short- and long-term analysis,
respectively, as in the work of Mickovski and van Beek (2009).
The elongation of an average diameter root for a 5 mm shear
displacement was calculated as 9.85 104 [mm/mm] from Eq. (4).
The mobilised root tensile strength at 5 mm displacement (i.e.
shear displacement at which the non-rooted soil strength reaches
its peak value) was calculated as 0.99 MPa (s in Table 2) which is
the synchronised root strength value. By using both this value and
the RAR at the shear surface in Eq. (6), the tensile strength of roots
per unit area of soil (tR) was obtained. Finally, the calculated value
of the synchronised added cohesion due to roots (Eq. (3)) was
0.47 kPa (Table 2). For the rooted soil simulation, this value was
added to the non-rooted soil cohesion shown in Table 1 for both
short- and long-term LE analysis of the slope stability.
Using Bishop’s LE method and the values in Table 2 shows a
global slope safety factor of 1.02 and 0.916 for the short- and longterm analysis, respectively (Fig. 7) i.e. a slight increase when
compared to the stability of the non-vegetated slope. The
associated critical slip surfaces were investigated in step 3 (local
safety factor check) of the proposed methodology.
3.3. Step 3
After the inspection, the critical slip surfaces were divided into
peak and residual zones based on the SFs calculated locally for each
slice. In the residual zone the roots were considered to be deforming
and mobilising their tensile strength until reaching their ultimate
tensile strength tR, which would yield the peak value of the root
reinforcement of as DS = 2.3 kPa (Eq. (3)). This value is the total
available strength value which is used in the numerator of Eq. (7).
For the slices with FSL < 1 and without any root reinforcement,
the difference between the actual applied stress and the soil
residual stress was considered to be transferred to the adjacent
slices (i.e. re-calculation of FSL for the affected slices using Eq. (7))
yielding the results shown in Table 3.
The comparison between the SFs obtained using the traditional
soil only approach (Mickovski and van Beek, 2009) and the new
proposed methodology are shown in Table 4.
4. Discussion
The comparison between the slope safety factor values
calculated using traditional geotechnical and eco-technological
engineering approaches shows that the effect of vegetation is very
important in the cases where the fallow slope is at risk of failure.
Relatively small RARs can contribute to minimal increase in the
resistance of the rooted soil which, in turn, can result in an increase
in safety factor. It is important to note that the traditional
application of global increase in soil cohesion due to the presence
of roots can lead to an overestimation of the stability of the slope in
the short-term (Table 4), i.e. at the time when the pore-water
pressures are built-up in the soil, there is no sufficient time for
drainage, and the resistance to shear failure mainly depends on the
mechanical effects of the roots (Mickovski et al., 2009; Schwarz
et al., 2010). For this case, the proposed methodology provides a
more conservative estimate of the slope stability which is also
more realistic and applicable wherever progressive failure
dominates the instability mechanism (Liu, 2009). For both
short-term (undrained) and long-term (drained) cases, the
magnitude of differences between the two approaches is offset
by the fact that the soil encountered on the case study site was
normally consolidated (natural slope) and, therefore, its peak and
residual values coincide (Smith and Smith, 1998). An analysis of a
slope comprising overconsolidated soil would have yielded results
with bigger differences between the approaches.
The SF value obtained for long-term analysis (drained
Fig. 7. Step 2 long- and short-term stability analyses including vetiver root effects (added cohesion = 0.47 kPa).
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G. Tardío, S.B. Mickovski / Ecological Engineering 82 (2015) 222–230
Table 3
Initial local safety factors (step 2), recalculated local safety factors (step 3–Eq. (7)) and the recalculated global safety factor (step 3–Eq. (9)). Long-term slope stability analysis
case.
Slice
Local SF
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1.1
1
1
1
1
1
0.98
0.93
0.89
0.85
0.82
0.78
0.77
0.75
New SF (Eq. (7))
Slice length (m)
Slice length/total length
(slice length/total length) local SF
1.51
1.7
1.65
1.36
1.25
1.16
1.16
1.16
Total length
0.14
0.14
0.12
0.12
0.12
0.13
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
1.65
0.08
0.08
0.07
0.07
0.07
0.08
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
New global safety factor
0.09
0.08
0.07
0.07
0.07
0.08
0.10
0.11
0.11
0.09
0.08
0.08
0.08
0.08
1.19
conditions) in the proposed methodology is higher than the one
obtained by Mickovski and van Beek (2009). This is partially due to
the fact that the critical slip surface analysed in this case is
relatively shallow due to the nature of the soil on site and, thus,
intercepts a larger number of roots with higher RAR. Furthermore,
in the case study the effects of the pore-water pressures were
negligible which, again, showed that the mechanical effects of the
roots on slope stability become predominant during the dry
periods.
The safety factors obtained in steps 2 and 3 of the proposed
methodology account for the stress transfer between the soil and
the roots which is not the case in the traditional stability analyses.
As the slope progressively fails and roots gain relevance in the
slope global stability, the safety factor increases its value (Table 4)
which is in contrast to the traditional analyses (Wu et al., 1979)
where the role of the roots is the same throughout the process. The
slope stability analyses in step 2 of the proposed methodology give
a lower SF values because the tensile stress used in the added
cohesion formula is not the ultimate root tensile strength but the
root strength value corresponding to the strain level at which the
soil reaches its peak strength value.
In our model, in the residual zones of the failure surface the role
of the flexible roots is very important as the available strength
mainly depends on the roots’ mechanical capacities due to their
lower rigidity when compared to the soil. This effect is intuitive
and coincides with the results obtained by Bourrier et al. (2013)
who found that the reinforcement effect of flexible roots was the
highest when the soil had developed its residual strength as in the
assumptions of our approach.
In this study we used the perpendicular root model for soil
reinforcement (Wu et al., 1979) based on the observed root
morphology and root failure mechanism during the in situ tests.
The use of this model, subject of criticisms due to potential
overestimation of root reinforcement (Preti and Giadrossich, 2009;
Mickovski et al., 2009), was justified by the comparable results of
the measured vs calculated shear resistance of the soil rooted with
vetiver roots (Mickovski and van Beek, 2009).
The main advantage of the proposed method is that it is generic
and allows the incorporation of different rooting models in the
stability assessment process. Root models such as Fibre Bundle
(FBM; e.g. Pollen and Simon, 2005) or Root Bundle (RBM; e.g.
Schwarz et al., 2010) and the phenomena such as lateral root
cohesion (Schwarz et al., 2010) can be incorporated in step 2 of the
proposed methodology for a known force-displacement behaviour
and used as an input into the LE methods for slope stability
assessment. In these cases, the root bundle force corresponding to
non-rooted soil peak displacement must be included in the
numerator of the SF formula along with the soil peak strength
values (step 2). At high displacement (strain) level, the peak root
bundle force must be included in the SF formula numerator and the
soil residual strength must be included in the SF denominator (step
3).
On the same lines, our method allows for stability assessment in
accordance with Eurocode 7 (EN ISO 1997) where partial factors
specified within the code can be applied to both peak and residual
soil strength values in steps 2 and 3 to verify the GEO limit state.
From this perspective, the calculations shown within this article
could be considered as calculations with the characteristic values
of both material and actions which, in the case of natural slopes, is
usually the first step in the assessment of stability.
Another advantage of the proposed methodology is the
incorporation of simulation of the stress transfer process and
the heterogeneous existing stress–strain state within the root–soil
continuum in the LE stability assessment (steps 2 and 3) based on
the mode of the observed slope failure in situ. The value of the
calculated stress mobilised by the roots (0.99 kPa) shows the
proportion (approx. 20%) of the total root tensile strength
(4.91 MPa) mobilised at the moment when the soil reaches its
peak shear strength value. This implies that for flexible roots,
during the first stages of shear, the soil strength dominates the
behaviour of the root soil composite. The value obtained compares
well with the shear test results on the rooted soil block (Mickovski
and van Beek, 2009) where there is a negligible difference in the
behaviour of rooted and unrooted soil up to the stage when the soil
reaches its peak value. At this point, the roots have been
Table 4
Comparisons between the safety factor (SF) values of the studied slope calculated with different approaches.
Slope stability (SF)
Short-term
Long-term
Mickovski and van Beek (2009)
Proposed methodology
Fallow soil
Rooted soil
Fallow soil
Rooted soil (step 2)
Rooted soil (step 3)
1.01
<1
1.13
1.06
1.01
<1
1.02
0.91
1.11
1.19
G. Tardío, S.B. Mickovski / Ecological Engineering 82 (2015) 222–230
straightened up (Schwarz et al., 2010) and the tensile strength
within them starts to be mobilised. However, in the calculations
this effect has been neglected due to the observed verticality of the
vetiver root system (Mickovski et al., 2005) and therefore the
results may be considered conservative.
The proposed methodology offers, through step 3, a chance to
investigate the potential critical zones where the sliding soil mass
would be the weakest and could be targeted for stabilisation with
other, potentially structural measures. The implementation of the
proposed methodology in existing slope stability software is
relatively straightforward and it offers insight into which parts of
the soil are contributing with their residual strength and in which
parts of the slope the vegetation is playing a major role in terms of
slope stability. The analysis of local safety factors also allows for a
deeper insight into stress transfer phenomenon and therefore
improves the safety factor calculation process.
The validation of the proposed methodology was limited to
particular soil conditions and fibrous root system. While this was
carried out due to practical reasons, i.e. availability of comparable
data, it also contributed towards confirmation of the benefits of the
fibrous root systems in providing reinforcement. The flexible
nature of the vetiver roots helped in preventing soil mass wasting
after a slip was initiated unlike, say, more rigid, structural roots
that would prevent slip initiation but would not necessarily
prevent mass wasting after the slip initiation (Duckett, 2014). The
potential analysis of more complex root architectures would
require incorporating both flexible and rigid root behaviour and
their respective contribution to reinforcement. Furthermore, more
simulations on different soil types with different overconsolidation ratios and other environmental settings will have to be carried
out in order to increase the confidence of the use of the proposed
methodology in eco-engineering applications.
5. Conclusions
The incorporation of root mechanical effects into the stability
assessment of vegetated slopes should take into account the
different pace at which soil and root strength is mobilised. Plant
root reinforcement effects cannot be only quantified as a constant
additional shear resistance of the soil as the available soil–root
composite shear resistance depends on the shear strain.
A methodology to harmonise these different mechanical
behaviours is proposed in order to achieve a more realistic
simulation of rooted soil composite materials. The methodology
combines stress–strain analysis, continuum mechanics and LE
stability assessment. For this methodology, the stress–strain
behaviour for both soil and reinforcement (roots) must be known
and compatibility sought in order to incorporate a realistic value of
the root reinforcement into a LE method for calculation of slope
stability.
The proposed methodology is validated by the findings of a field
study incorporating measurements and observations on soil as
well as the plant root morphology and physical characteristic
(Mickovski and van Beek, 2009). In both approaches, as the shear
displacements (strain) increase, the stress transfer processes
between the soil and vetiver roots is well represented by the
obtained numerical results. The results of the simulation show
more conservative and realistic results for the stability of a
vegetated slope immediately after a precipitation event when
progressive failure is most likely to be triggered.
With the proposed methodology, a better simulation of the
progressive failure phenomenon is included in traditional slope
stability analysis showing that the safety factor calculation is not
stress–strain independent. Furthermore, the proposed methodology gives an insight into the root reinforcement effect distribution
229
along the slip surfaces, failure mechanism, and synchronised
behaviour of both root and soil.
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